A Survey of Intuitionistic Descriptive Set Theory

In descriptive set theory (cf. Moschovakis 1980), a subject which was founded in the early decades of this century by French and Russian mathematicians like Baire, Borel, Lebesgue, Lusin and Suslin, one describes and studies classes of subsets of the set IR of real numbers. Examples of such classes are: the class of open subsets of IR, the class of closed subsets of IR, the class of those subsets of IR which are the union of a countable sequence of closed subsets of IR, and its dual: the class of those subsets of IR which are the intersection of a countable sequence of open subsets of IR,…, the class of Borel subsets of IR, i.e.: the least class of subsets of IR which contains the closed subsets of IR and the open subsets of IR and is closed under the operations of countable union and countable intersection, the class of analytical subsets of IR, i.e.: the class of those subsets of IR that result from projecting a closed subset of IR2 on one of the coordinate-axes, the class of co-analytical subsets of IR, i.e.: the class of those subsets of IR whose complement is analytical,…, the class of projective subsets of IR, i.e.: the class of those subsets of IR which result from a closed subset of some IRn by a finite number of applications of the operations of projection and complementation.